Lecture6 - CS221 Lecture notes Supervised learning So far...

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Unformatted text preview: CS221 Lecture notes Supervised learning So far in this course, we have only considered problems where the entire state of the world is known in advance. Rarely, however, can we completely specify the state of the world a priori, so often the agent must be able to learn about the world from actual observations. For instance, we might be interested in automatically distinguishing different handwritten digits. Its hard for us to formally state a set of rules which distinguish handwritten 2s from 5s, and so we cant simply program it directly into the computer. Rather, we will have an algorithm automatically figure it out from data. The general set of techniques for doing this is known as machine learning . Since machine learning is such a broad field, there is no single definition that everybody agrees upon, but here are some attempts: Machine learning is the field of study that gives computers the ability to learn without being explicitly programmed. 1 A computer program is said to learn from experience E with respect to some task T and some performance measure P if its performance on T, as measured by P, improves with experience E. 2 An example of an early machine learning program was Arthur Samuels chess playing program, which learned to play checkers by playing many games against itself, and eventually learned to play much better than Samuel him- self. Since them, machine learning has produced many practical applications. For the next two lectures, we will focus on supervised learning , where our algorithm will work with labeled training examples, or examples which 1 Arthur, S. Some studies in machine learning using the game of checkers. IBM Journal (3): 210-229. 2 Mitchell, T. Machine Learning. McGraw-Hill, 1997. 1 2 are labeled with the property we are trying to predict. For instance, if we are trying to classify handwritten digits, labeled data would constitute image files which are labeled by humans as being a particular digit. 1 Linear regression As a motivating example, suppose we have a dataset giving the living areas and prices of 47 houses from Portland, Oregon: Living area (feet 2 ) Price (1000$s) 2104 400 1600 330 2400 369 1416 232 3000 540 . . . . . . We can plot this data: 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 100 200 300 400 500 600 700 800 900 1000 housing prices square feet price (in $1000) Given data like this, how can we learn to predict the prices of other houses in Portland, as a function of the size of their living areas? To establish notation for future use, well use x ( i ) to denote the input variables (living area in this example), also called input features , and y ( i ) to denote the output or target variable that we are trying to predict (price). A pair ( x ( i ) , y ( i ) ) is called a training example , and the dataset that well be using to learna list of m training examples { ( x ( i ) , y ( i ) ); i = 1 , . . ., m } is called a training set . Note that the superscript ( i ) in the 3...
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Lecture6 - CS221 Lecture notes Supervised learning So far...

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